The Parallel Performance and Implementation of an Adaptive Multigrid Algorithm

An adaptive multigrid algorithm has been implemented on shared memory parallel computers to solve large-scale structural mechanics problems. The solution algorithm begins by solving the problem on the initial mesh, refining this mesh as required by the chosen adaptive scheme, and then solving the problem on the new mesh using the multigrid method and all of the previous meshes. This procedure is repeated until a sufficiently fine mesh is produced that meets the specified error tolerance. A very general scheme has been proposed to impose multi-point constraints in such a way that the parallel nature of the multigrid algorithm is maintained. The matrix-vector operations involved in the multigrid algorithm have been computed in a three stage process, each of which are performed on an element level and are fully optimized by processing blocks of elements in vector-concurrent mode. The element-by-element computations reduce the requirements on storage and are easy to parallelize. Numerical results indicate that the computational effort is approximately linearly proportional to the problem size. Maximum speed-ups of around 3.75 were achieved on a 4 processor Convex, indicating that almost 98% of the solution algorithm has been parallelized. The convergence behavior of the multigrid cycles was also studied and results obtained suggest a new approach, based on the value of the global relative percent error, for terminating multigrid iterations on a given mesh.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Civil Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Misra, Himanshu

Contributors dc:contributor

• Parsons, Ian D.,

• Applied Mechanics
• Engineering, Civil
• Engineering, Mechanical

Identifier

(UMI)AAI9411718

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/72209